For a body rotating about a fixed axis

PHYSICS · Subjective · A Level · Physics · Engineering physics · Engineering physics

Problem

For a body rotating about a fixed axis, its angular displacement as a function of time is given by

\theta = 4t^{2} + 2t + 1

(in radians) for

0 \le t \le 6\,\text{s}

. (i) Obtain expressions for its instantaneous angular velocity

\omega(t)

and angular acceleration

\alpha(t)

. (ii) Find the numerical values of

\omega

and

\alpha

t = 3\,\text{s}

. (iii) Draw a clearly labelled

\omega

–

t

graph for the interval

0

6\,\text{s}

. (iv) Using any convenient method, compute the total angle turned during the

6\,\text{s}

and verify that it matches the result obtained directly from the given

\theta(t)

expression.